SINGULAR INTEGRAL EQUATIONS WITH COSECANT KERNEL IN SOLUTIONS WITH SINGULARITIES OF ORDER ONE*

In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc along closed smooth contours restricted in the strip 0 < Rez < aπ is discussed. Finally, the solutions with singularities of order one for the above two problems are discussed.